Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
354 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #31771312 | C2 | semidirect |
| 3. #31771010 | C2 | semidirect |
| 4. #31770947 | C2 | semidirect |
| 5. #31770919 | C2 | semidirect |
| 6. #31770901 | C2 | semidirect |
| 7. #31770896 | C2 | semidirect |
| 8. #31770851 | C2 | semidirect |
| 9. C4×#16864391 | C2 | semidirect |
| 10. #31770647 | C2 | semidirect |
| 11. #436×C269 | C2 | semidirect |
| 121. C269 | #3357 | semidirect |
| 132. #436 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771320 | 2 |
| #31771312 | 2 |
| #31771010 | 2 |
| #31770947 | 2 |
| #31770919 | 2 |
| #31770901 | 2 |
| #31770896 | 2 |
| #31770851 | 2 |
| C4×#16864391 | 2 |
| #31770647 | 2 |
| #436×C269 | 2 |
| #3357 | 269 |